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LINEAR PROGRAMMING & PRODUCT MIX

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USING THE DATA BELOW, PLEASE ASSIST WITH QUESTIONS 1 THRU 4:

YOUR COMPANY PRODUCES 2 PRODUCTS - MODEL A & MODEL B. THESE MODELS HAVE PROFITS OF $1000 & $2000 RESPECTIVELY. EACH MODEL IS PRODUCED IN A 3 STEP PROCESS. THE AMOUNT OF TIME USED BY EACH MODEL IN EACH PROCESS IS:
MODEL A MODEL B TOTAL TIME AVAILABLE
PROCESS 1 1 3 150
PROCESS 2 3 3 210
PROCESS 3 2 1 120

1) SKETCH THE SET THAT SHOWS THE COMBINATION OF MODEL A & MODEL B THAT CAN BE PRODUCED (FEASIBLE SET)

2) SKETCH OUT A FAMILY OF CONTOUR LINES THAT SHOW VARIOUS COMBINATIONS OF MODEL A AND MODEL B THAT WILL PRODUCE PROFIT OF $100,000 & $140,000

3) FIND THE COMBINATION OF MODEL A & MODEL B THAT MAXIMIZES THE FIRM'S PROFIT. WHAT IS THE FIRM'S PROFIT AT THIS PRODUCT MIX?

4) IF YOU COULD BUY EXTRA CAPACITY OF PROCESS 3, WHAT IS THE MOST THAT YOU WOULD BE WILLING TO PAY TO PURCHASE IT? PLEASE SHOW WORK & PROVIDE AN EXPLANATION.

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https://brainmass.com/economics/finance/linear-programming-product-mix-146276

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Let x1 and x2 be the units of Model A and Model B produced ...

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LINEAR PROGRAMMING & PRODUCT MIX guidance is offered.

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Linear Programming : Optimizing Product Mix

The Androgynous Bicycle Company (ABC) has the hottest new products on the upscale toy market -- boys' and girls' bicycles in bright fashion colors, with oversized hubs and axles, shell design safety tires, a strong padded frame, chrome-plated chains, brackets and valves, and a non-slip handlebar. Due to the seller's market for high-quality toys, ABC can sell all the bicycles it manufactures at the following prices: boys' bikes -- $220, girls' bikes -- $175. This is the price payable to ABC at its Orlando plant.

The firm's accountant has determined that direct labor costs will be 45% of the price ABC receives for the boys' model and 40% of the price received for the girls' model. Production costs other than labor, but excluding painting and packaging, are $44 per boys' bicycle and $30 per girls' bicycle. Painting and packaging are $20 per bike, regardless of model.

The Orlando plant's overall production capacity is 390 bicycles per day. Each boy's bike requires 2.5 labor hours while each girl's model takes 2.4 hours to complete. ABC currently employs 120 workers, who each work an 8-hour day. The firm has no desire to hire or fire employees to affect labor availability, believing its stable work force is one of its biggest assets.

a. Formulate a linear programming model that can be used to develop a product mix for the company that yields an optimal profit contribution.
b. Determine the optimal product mix using the Management Scientist software.
c. Explain the impact (if any) on the optimal solution resulting from the stable workforce policy adopted by the firm.

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